"All that glitters" or "Not all that glitters"?

In the phrase finder (http://www.phrases.org.uk/meanings/all-that-glitters-is-not-gold.html) I found the "correct" syntax of the saying: "All that glitters is not gold," and that’s fine. The saying trips off the tongue quite nicely, I guess, which is good in and of itself.

I’ve also read the OP’s question at "All that is gold does not glitter", which does not really pertain to my question, which is this:

How does the logically "wrong" syntax become accepted and traditional?

In other words, for other than purely stylistic reasons, is there a mini-theory which explains the phenomenon?

I realize that people prefer on purely stylistic grounds the peculiar syntax of a given saying or quotation. As I said, sometimes the way that words come trippingly off our tongues is sufficient reason for embracing a saying exactly as worded. I also realize that some sayings become accepted into the repertory of a culture’s proverbs by simply being repeated over the span of generations.

Nevertheless, despite its seeming almost fungible with "All that glitters is not gold," "Not all that glitters is gold" is preferable, logically, is it not? After all, if gold is NOT among all things that glitter, then why does it glitter? I mean, it does glitter, doesn’t it?

Perhaps I’m making too big a deal of this. Perhaps it’s a non-issue. Perhaps language just evolves that way sometimes, and there is nothing necessarily illogical or irrational about it. Even if there is something illogical or seemingly irrational about it, language is, after all, illogical (if not irrational) at times. As the young people say today in their quasi-profound, ersatz way, "It is what it is."

To wrap things up, I’ve posed at least three questions:

Does the basis for an answer to my question come from people’s stylistic preferences?

Does the basis for an answer to my question come from the phenomenon of perseveration? Or,

Does the basis for an answer to my question come from some other explanation (or a combination of question one and question two and some other explanation)?

If I get one down vote, I’ll delete the post, but I’m really curious about this!